Exact Solution of the Class-E Inverter for Wireless Power Transfer Systems

Bruna C. Nicoletti; Fábio Ecke Bisogno; Lucas S. Mendonça

doi:10.18618/REP.e202542

Authors

Bruna C. Nicoletti Federal University of Technology of Paraná https://orcid.org/0009-0005-9471-6062
Fábio Ecke Bisogno Koblenz University of Applied Sciences
Lucas S. Mendonça Universidade Tecnológica Federal do Paraná https://orcid.org/0000-0002-4927-6206

DOI:

https://doi.org/10.18618/REP.e202542

Keywords:

dc-ac inverters, resonant converters, wireless power transfer

Abstract

This paper introduces the exact solution of the Class-E WPT resonant inverter. Dominantly, the DC-AC inverters for WPT systems are analyzed by assuming a sinusoid waveform for the output variables. However, by allowing waveform light distortions, the magnetic element values can be reduced; which is provided by the proposed method. It is shown that the circuit waveforms are composed of sine, cosine and exponential terms. The obtained solutions are used to design a 500 kHz Class-E WPT resonant inverter which operates with ZVS. The design is experimentally verified and 74 % efficiency with 9.7 W output power is achieved.

Downloads

Download data is not yet available.

Author Biographies

Bruna C. Nicoletti, Federal University of Technology of Paraná

is a mechatronics engineer (2025) with the Federal University of Technology-Paraná. She currently works in software quality. Her areas of interest are: pwm and resonant converters.

Fábio Ecke Bisogno, Koblenz University of Applied Sciences

is an electrical engineer (1999), master (2001) in Electrical Engineering with the Federal University of Santa Maria, and doctor in Electrical Engineering with the Technische Universität Chemnitz (2006). He is currently a professor at Hochschule Koblenz. His areas of interest are: resonant converters, self-oscillating electronic converters and artificial lighting.

Lucas S. Mendonça, Universidade Tecnológica Federal do Paraná

is a control and automation engineer (2015), master (2017) and doctor in Electrical Engineering (2021) with the Federal University of Santa Maria. He is currently a professor at Federal University of Technology-Paraná. His areas of interest are: resonant and pwm dc-dc converters, ac-dc resonant rectifiers and dc-ac resonant inverters.

References

F. T. Carneiro, I. Barbi, “Análise, Projeto e Implementação de um Conversor com Transferencia de Energia Sem Fio para Carregadores de Baterias de Veículos Elétricos”, Eletrônica de Potência, vol. 26, no. 3, pp. 260–267, September 2021. DOI: https://doi.org/10.18618/REP.2021.3.0003

R. B. Godoy, E. T. Maddalena, G. de F. Lima, L. F. F. abd V. L. V. Torres, J. O. P. Pinto, “Wireless Charging System With a Nonconventional Compensation Topology for Electric Vehicles and Other Applications”, Eletrônica de Potência, vol. 21, no. 1, pp. 42–51, March 2016. DOI: https://doi.org/10.18618/REP.2016.1.2575

D. S. Yeole, A. J. Anil, C. P. Pandit, G. V. Vinayak, “Analysis of Compensation Network in Resonant Inductive Power Transfer (RIPT) for Electric Vehicle Charging”, in 2025 5th International Conference on Trends in Material Science and Inventive Materials (ICTMIM), pp. 134–137, 2025. DOI: https://doi.org/10.1109/ICTMIM65579.2025.10988014

C. Zhang, N. Tang, W. Zhong, C. K. Lee, R. S. Y. Hui, “A new energy harvesting and wireless power transfer system for Smart Grid”, in 2016 IEEE 7th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), pp. 1–5, 2016. DOI: https://doi.org/10.1109/PEDG.2016.7527006

J.-Q. Zhu, Y.-L. Ban, Y. Zhang, Z. Yan, R.-M. Xu, C. C. Mi, “Three-Coil Wireless Charging System for Metal-Cover Smartphone Applications”, IEEE Transactions on Power Electronics, vol. 35, no. 5, pp. 4847–4858, 2020. DOI: https://doi.org/10.1109/TPEL.2019.2944845

J. Wu, D. Lan, X. Yu, Y. Zheng, R. Xie, Y. Zhang, “An Inductive and Capacitive Hybrid Wireless Power Transfer System for Consumer Electronics with Shared Components”, in 2024 3rd International Conference on Smart Grids and Energy Systems (SGES), pp. 86–89, 2024. DOI: https://doi.org/10.1109/SGES63808.2024.10824149

Z. Liang, J. Wang, Y. Zhang, J. Jiang, Z. Yan, C. Mi, “A Compact Spatial Free-Positioning Wireless Charging System for Consumer Electronics Using a Three-Dimensional Transmitting Coil”, Energies, vol. 12, no. 8, 2019. DOI: https://doi.org/10.3390/en12081409

G. L. Barbruni, F. Rodino, P. M. Ros, D. Demarchi, D. Ghezzi, S. Carrara, “A Wearable Real-Time System for Simultaneous Wireless Power and Data Transmission to Cortical Visual Prosthesis”, IEEE Transactions on Biomedical Circuits and Systems, vol. 18, no. 3, pp. 580–591, 2024. DOI: https://doi.org/10.1109/TBCAS.2024.3357626

M. A. de Rooij, “The ZVS voltage-mode class-D amplifier, an eGaN® FET-enabled topology for highly resonant wireless energy transfer”, in 2015 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 1608–1613, 2015. DOI: https://doi.org/10.1109/APEC.2015.7104562

M. d. Rooij, “Performance Comparison for A4WP Class-3 Wireless Power Compliance between eGaN FET and MOSFET in a ZVS Class D Amplifier”, in Proceedings of PCIM Europe 2015; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, pp. 1–8, 2015.

S.-A. El-Hamamsy, “Design of high-efficiency RF Class-D power amplifier”, IEEE Transactions on Power Electronics, vol. 9, no. 3, pp. 297–308, 1994. DOI: https://doi.org/10.1109/63.311263

X. Wei, H. Sekiya, T. Nagashima, M. K. Kazimierczuk, T. Suetsugu, “Steady-State Analysis and Design of Class-D ZVS Inverter at Any Duty Ratio”, IEEE Transactions on Power Electronics, vol. 31, no. 1, pp. 394–405, 2016. DOI: https://doi.org/10.1109/TPEL.2015.2400463

Z. Shu, Y. Fengfa, W. Yijie, J. M. Alonso, “A 500-kHz ZVS ClassE Type DC–DC Converter With Two Anti-Series mosfets Topology”, IEEE Transactions on Power Electronics, vol. 38, no. 9, pp. 10810– 10820, September 2020. DOI: https://doi.org/10.1109/TPEL.2023.3287161

M. K. Kazimierczuk, J. Jozwik, “Resonant DC/DC Converter with Class-E Inverter and Class-E Rectifier”, IEEE Transactions on Industrial Electronics, vol. 36, no. 4, pp. 468–478, November 1989. DOI: https://doi.org/10.1109/41.43017

T. Nagashima, X. Wei, E. Bou, E. Alarcon, M. K. Kazimierczuk, ´ H. Sekiya, “Analysis and Design of Loosely Inductive Coupled Wireless Power Transfer System Based on Class-E2 DC-DC Converter for Efficiency Enhancement”, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 62, no. 11, pp. 2781–2791, November 2015. DOI: https://doi.org/10.1109/TCSI.2015.2482338

T. Sensui, H. Koizumi, “Load-Independent Class E Zero-Voltage Switching Parallel Resonant Inverter”, IEEE Transactions on Power Electronics, vol. 36, no. 11, pp. 12805–12818, 2021. DOI: https://doi.org/10.1109/TPEL.2021.3077077

A. Komanaka, W. Zhu, X. Wei, K. Nguyen, H. Sekiya, “Load Independent Inverse Class-E ZVS Inverter and its Application to Wireless Power Transfer Systems”, IET Power Electronics, vol. 15, no. 7, pp. 644–658, 2022. DOI: https://doi.org/10.1049/pel2.12256

S. Aldhaher, D. C. Yates, P. D. Mitcheson, “Load-Independent Class E/EF Inverters and Rectifiers for MHz-Switching Applications”, IEEE Transactions on Power Electronics, vol. 33, no. 10, pp. 8270–8287, 2018. DOI: https://doi.org/10.1109/TPEL.2018.2813760

P. Chen, S. He, “Analysis of Inverse Class-E Power Amplifier at Subnominal Condition With 50% Duty Ratio”, IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 62, no. 4, pp. 342–346, 2015. DOI: https://doi.org/10.1109/TCSII.2014.2387655

T. Nagashima, X. Wei, E. Bou, E. Alarcon, H. Sekiya, “Analytical ´ Design for Resonant Inductive Coupling Wireless Power Transfer System with Class-E Inverter and Class-DE Rectifier”, in 2015 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 686– 689, 2015. DOI: https://doi.org/10.1109/ISCAS.2015.7168726

H. Sekiya, X. Wei, T. Nagashima, M. K. Kazimierczuk, “Steady-State Analysis and Design of Class-DE Inverter at Any Duty Ratio”, IEEE Transactions on Power Electronics, vol. 30, no. 7, pp. 3685–3694, 2015. DOI: https://doi.org/10.1109/TPEL.2014.2339355

J. Zhang, J. Zhao, L. Mao, J. Zhao, Z. Jiang, K. Qu, “ZVS Operation of Class-E Inverter Based on Secondary Side Zero Compensation Switching at Variable Coupling Coefficient in WPT”, IEEE Transactions on Industry Applications, vol. 58, no. 1, pp. 1022–1031, 2022. DOI: https://doi.org/10.1109/TIA.2021.3125916

C. Cheng, Y. Zhang, X. Zheng, W. Hua, “A Full-Range Soft-Switching Class-E Inverter Achieving Quasi-Constant Voltage Output”, IEEE Transactions on Power Electronics, vol. 40, no. 6, pp. 7663–7667, 2025. DOI: https://doi.org/10.1109/TPEL.2025.3541206

F. Bennia, A. Boudouda, “Wireless Power Transfer Optimization Using FEM-GA Method”, in 2024 3rd International Conference on Advanced Electrical Engineering (ICAEE), pp. 1–6, 2024. DOI: https://doi.org/10.1109/ICAEE61760.2024.10783287

M. Jarret, S. Newman, L. Goodman, I. Suzuki, M. Suzuki, “Measurement of mutual inductance from frequency dependence of impedance of AC coupled circuit using digital dual-phase lock-in amplifier”, American Journal of Physics, vol. 76, 07 2006.

Y. Wang, W. Liu, Y. Huangfu, “A Primary-Sided CLC Compensated Wireless Power Transfer System Based on the Class D Amplifier”, in IECON 2018 - 44th Annual Conference of the IEEE Industrial Electronics Society, pp. 943–947, 2018. DOI: https://doi.org/10.1109/IECON.2018.8591707

H. Tebianian, Y. Salami, B. Jeyasurya, J. E. Quaicoe, “A 13.56-MHz Full-Bridge Class-D ZVS Inverter With Dynamic Dead-Time Control for Wireless Power Transfer Systems”, IEEE Transactions on Industrial Electronics, vol. 67, no. 2, pp. 1487–1497, 2020. DOI: https://doi.org/10.1109/TIE.2018.2890505